Earth’s atmospheric pressure p is oftenmodeled by assuming that the rate dp/dh at which p changeswith the altitude h above sea level is proportional to p. Supposethat the pressure at sea level is 1013 millibars (about 14.7 poundsper square inch) and that the pressure at an altitude of 20 km is90 millibars. Solve the initial value problemDifferential equation: dp/dh = kp (k a constant)Initial condition: p = p0 when h = 0to express p in terms of h. Determine the values of p0 and kfrom the given altitude-pressure data.

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A:

Q: A particle is moving along the x-axis so that its position at time t≥0 is given by the equation…

A:

Q: If a substance decomposes at a rate proportional to the amount of the substance present, and the…

A: This question is based on application of diffrential equation.

Q: (2) From assumption (c), the velocity (v) at time (t) of the water droplet is 3. v' + t+ro If the…

A: This is a linear differential equation which have to be solved using integrating factor

Q: A mass m is accelerated by a time-varying force exp(-ßt)v², where v is its velocity. It also…

A:

Q: According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot…

A:

Q: A projectile fired from the point (0,0) at an angle to the positive x-axis has a trajectory given by…

A: GivenProjectile fired equation y= Cx-(1+C2)(g2)(xv2) ...(1)According to question g=9.81…

Q: A projectile fired from the point (0,0) at an angle to the positive x-axis has a trajectory given by…

A: A projectile from the point (0,0) at an angle to the positive x-axis has a trajectory given by…

Q: 1. A particle moves along the x-axis according to the equation x-2+3F, where x is in m and is in…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s?, where k is a…

A:

Q: The average energy E (in kcal) needed for a lizard to walk or run a distance of 1 km has been…

A: Energy needed for a lizard to walk or run a distance of 1 km is modeled by the below equation. Here…

Q: A materials scientist is experimenting with a new material with which to make beverage cans. She…

A: From the given plots, the scatterplot shows a perfect negative relationship between the variables.…

Q: A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following…

A:

Q: A rectangular swimming pool 10 ft wide by 20 ft long and of uniform depth is being filled with…

A: Given that, Width of rectangular swimming pool = 10 ft Length of rectangular swimming pool = 20 ft…

Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s2, where k is a…

A: use simple velocity,acceration,and distance formula.

Q: The rate at which a ceratin disease spreads is proportional to the product of the percentage of the…

A: We have to find the rate R(t) at which disease spreads Constant of  Proportionality = 0.03 Percent…

Q: dv dt    = −kv2 An object moving through the water has an initial velocity of 40 m/s. Two seconds…

A: As the given differential equation is: dvdt=-kv2 Given conditions are:  t=0 , v=40 mst=2s, v=30 ms…

Q: A cylindrical tank as shown in Figure Q 1 is initially filled with water to a height, ho (m). The…

A: Solution:

Q: 1. If a stone is thrown vertically upward frosthe surface of the moon with a velocity of 10 meters…

A: Follow the procedure given below.

Q: According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot…

A: We need to find error.

Q: 12. If a substance decomposes at a rate proportional to the amount of the substance present, and the…

A:

Q: The barometric pressure p (in inches of mercury) at an altitude x miles above sea level satisfies…

A:

Q: b) The mass (in kg) of a product from a chemical reaction is denoted by 'y'. The dy rate at which…

A: b Separate the terms of both the variables Then let 1+y2=z2ydy=dzand 1+t2=u22tdt=2udu

Q: A ball is thrown upward from a height of 12.5 m at an initial speed of 30 m/sec. Acceleration…

A: Consider the height: H=12.5 m and initial speed: u=30m/sec The velocity function is given by v(t)=…

Q: Let C(t) be the concentration of a drug in the bloodstream. As the body eliminates the drug, C(t)…

A: Given, C’(t) = kC(t) We have to calculate the concentration at time t also calculate the time when…

Q: The marriage rate in a certain country in 1990 was 0.95%, and there were about 351,000 marriages…

A: 1990 corresponds to t=0 So, M0= 351000 And r= 0.95% = 0.0095 So the model is:

Q: If the brakes on a car give the car a constant negative acceleration of 24 m/s2, where is a positive…

A:

Q: Suppose that an lowa class battleship has mass around 54,000 metric tons (54,000,000 kg) and a…

A:

Q: A rocket accelerates by burning its on-board fuel, so its mass decreases with time. Suppose the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The volume (v) of a sphere varies directly with the cube of its radius (r). If k is the constant of…

A:

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A:

Q: 2. A firefighter who weighs \(192\) lb slides down an infinitely long fire pole that exerts a…

A:

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. (a) (3 marks). A 5ft tall…

A:

Q: The equation of motion of a mass is given as: y = (0.51)e 0.-(0.01)e0.2, where y is the displacement…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: In a series resistance-capacitance DC circuit, the instantaneous charge Q on the capacitor as a…

A:

Q: 4. The position of an object at time t is given by x = 34f - 8t + 2, where x is in feet and t is in…

A:

Q: Given the acceleration of an object and its initial velocity, how doyou find the velocity of the…

A: We know that the rate of change of velocity of a moving particle is known as its acceleration. Let…

Q: When a vertical beam of light passes through a transparent medium, the rate at which its intensity I…

A:

Q: A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the…

A: you can clearly understand if you follow the below solution

Q: At what speed should a fish swim upstream so as to reach its destination with the least expenditure…

A:

Q: If the position of a particle of mass m at time t seconds is given by 7= (r +1)i- 2j + ik, which of…

A: The position vector of the particle is given by, r→=t2+1i−2tj+t2k

Q: The velocity of a particle in reference frame A is (4.0 î + 5.0 f) m/s. The velocity of reference…

A: Given: velocity of a particle with respect to frame A=4i+5j  velocity of frame A with respect to…

Q: The Darcy–Weisbach equation states that the power-generating capacity in a hydroelectric system that…

A:

Q: The velocity function of a particle moving along a horizontal line is given by v(t) = ln 2 · 23t,…

A: The Velocity function of the particle moving along a horizontal line is given by v(t)=ln2·23t…

Q: A mass m is accelerated by a time-varying force exp(-ßt )v², where v is its velocity. It also…

A:

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A: Given : pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of amole…

Q: A particle that moves along a straight line has velocity v(t) = t?e meters per second after t…

A: The displacement -velocity -time equation is given by, dsdt=v(t) The displacement during the first t…

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Suppose a raindrop evaporates as it falls but maintains its spherical shape. Assume that the rate at…

A: (1) Mass of the raindrop is equal to the product of density and volume. Thus, determine the initial…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.